letters not visible in window picker with vim._core.ui2 and laststatus=3

Description

When using require'vim._core.ui2'.enable{}; vim.o.laststatus=3 the letters of the window picker do not get displayed.

Neovim version

NVIM v0.12.2
Build type: RelWithDebInfo
LuaJIT 2.1.1774896198

Operating system and version

6.19.14-arch1-1 Archlinux

Windows variant

No response

nvim-tree version

latest

Clean room replication

require'nvim-tree'.setup{actions = {open_file = { window_picker = { enable = true } }}}
require'vim._core.ui2'.enable{}
vim.o.laststatus=3

Steps to reproduce

1. nvim
2. :vsplit
3. :NvimTreeToggle
4. open a file

Expected behavior

the letters should be visible no matter the laststatus setting even with the new ui.

Actual behavior

Note: this is so weird that it may be an issue of neovim, but I don't know how to find out.

with laststatus=3 the statusline appears as the last line of the window and the cmdline appears above it. The statusline is completely blank instead of containing the letters hinting at which window is which.

The issue is only in the bottom statusline - top window of hsplit shows the letter correctly.

I've managed to get the statusline bugged once also with laststatus=1 so that it was swapped with the cmdline, so it likely is sth with neovim. But I don't know what function nvimtree uses to pick the windows, so I don't know how to reproduce it to report it in nvim

Reproduce the issue with nvim-tree setup, vim._core.ui2.enable{}, laststatus=3, :vsplit, :NvimTreeToggle, and opening a file. Start by tracing the window-picker path that renders its letters and compare the bottom statusline with the top hsplit window. Done means the picker letters remain visible with the new UI and laststatus settings, with the existing reproduction steps passing.